The original problem is:If a, b, c, d are the position vectors of points A,...

on2t1inf8b

on2t1inf8b

Answered

2022-07-20

The original problem is:
If a, b, c, d are the position vectors of points A, B, C, D respectively such that
( a d ) . ( b c ) = ( b d ) . ( c a ) = 0
then prove that D is the orthocentre of Δ ABC.
How do we go about proving that a point is the orthocentre of a triangle? I've tried expanding the dot product but I don't seem to get anywhere.

Answer & Explanation

kuglatid4

kuglatid4

Expert

2022-07-21Added 12 answers

That formula states that A D B C (so that D is on the altitude from A to B C) and that A C B D (so that D is on the altitude from B to A C). As D is on two altitudes of the triangle, it is its orthocentre.

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